{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model Checking\n",
    "\n",
    "After running an MCMC simulation, `sample` returns a `MultiTrace` object containing the samples for all the stochastic and deterministic random variables. The final step in Bayesian computation is model checking, which uses information from the sample to ensure that inferences derived from them are valid. \n",
    "\n",
    "There are two components to model checking:\n",
    "\n",
    "1. Convergence diagnostics\n",
    "2. Goodness of fit\n",
    "\n",
    "Convergence diagnostics are intended to detect lack of convergence in the Markov chain Monte Carlo sample; it is used to ensure that you have not halted your sampling too early. However, a converged model is not guaranteed to be a good model. \n",
    "\n",
    "Goodness of fit, is used to check the internal validity of the model, by comparing predictions from the model to the data used to fit the model. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convergence Diagnostics\n",
    "\n",
    "Valid inferences from sequences of MCMC samples are based on the\n",
    "assumption that the samples are derived from the true posterior\n",
    "distribution of interest. Theory guarantees this condition as the number\n",
    "of iterations approaches infinity. It is important, therefore, to\n",
    "determine the **minimum number of samples** required to ensure a reasonable\n",
    "approximation to the target posterior density. Unfortunately, no\n",
    "universal threshold exists across all problems, so convergence must be\n",
    "assessed independently each time MCMC estimation is performed. The\n",
    "procedures for verifying convergence are collectively known as\n",
    "*convergence diagnostics*.\n",
    "\n",
    "The most common approach to diagnosing convergence is a\n",
    "**statistical** approach, which uses metrics related the statistical properties of the observed chain. Reliance on the sample alone restricts such convergence\n",
    "criteria to **heuristics**. As a result, convergence cannot be guaranteed.\n",
    "Although evidence for lack of convergence using statistical convergence\n",
    "diagnostics will correctly imply lack of convergence in the chain, the\n",
    "absence of such evidence will not *guarantee* convergence in the chain.\n",
    "Nevertheless, negative results for one or more criteria may provide some\n",
    "measure of assurance to users that their sample will provide valid\n",
    "inferences.\n",
    "\n",
    "For most simple models, convergence will occur quickly, sometimes within\n",
    "a the first several hundred iterations, after which all remaining\n",
    "samples of the chain may be used to calculate posterior quantities. For\n",
    "more complex models, convergence requires a significantly longer burn-in\n",
    "period; sometimes orders of magnitude more samples are needed.\n",
    "Frequently, lack of convergence will be caused by **poor mixing**. \n",
    "Recall that *mixing* refers to the degree to which the Markov\n",
    "chain explores the support of the posterior distribution. Poor mixing\n",
    "may stem from inappropriate proposals (if one is using the\n",
    "Metropolis-Hastings sampler) or from attempting to estimate models with\n",
    "highly correlated variables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Rat growth\n",
    "\n",
    "This example is taken from section 6 of Gelfand et al (1990), and concerns 30 young rats whose weights were measured weekly for five weeks. So, $Y_{i,j}$ is the weight of the $i$th rat measured at age $x_j$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "import warnings\n",
    "warnings.simplefilter('ignore')\n",
    "\n",
    "sns.set_context('notebook')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>8.0</th>\n",
       "      <th>15.0</th>\n",
       "      <th>22.0</th>\n",
       "      <th>29.0</th>\n",
       "      <th>36.0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>151</td>\n",
       "      <td>199</td>\n",
       "      <td>246</td>\n",
       "      <td>283</td>\n",
       "      <td>320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>145</td>\n",
       "      <td>199</td>\n",
       "      <td>249</td>\n",
       "      <td>293</td>\n",
       "      <td>354</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>147</td>\n",
       "      <td>214</td>\n",
       "      <td>263</td>\n",
       "      <td>312</td>\n",
       "      <td>328</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>155</td>\n",
       "      <td>200</td>\n",
       "      <td>237</td>\n",
       "      <td>272</td>\n",
       "      <td>297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>135</td>\n",
       "      <td>188</td>\n",
       "      <td>230</td>\n",
       "      <td>280</td>\n",
       "      <td>323</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   8.0   15.0  22.0  29.0  36.0\n",
       "0   151   199   246   283   320\n",
       "1   145   199   249   293   354\n",
       "2   147   214   263   312   328\n",
       "3   155   200   237   272   297\n",
       "4   135   188   230   280   323"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ages = 8.0, 15.0, 22.0, 29.0, 36.0\n",
    "rat_weights = pd.DataFrame(np.array([151, 199, 246, 283, 320,\n",
    "                     145, 199, 249, 293, 354,\n",
    "                     147, 214, 263, 312, 328,\n",
    "                     155, 200, 237, 272, 297,\n",
    "                     135, 188, 230, 280, 323,\n",
    "                     159, 210, 252, 298, 331,\n",
    "                     141, 189, 231, 275, 305,\n",
    "                     159, 201, 248, 297, 338,\n",
    "                     177, 236, 285, 350, 376,\n",
    "                     134, 182, 220, 260, 296,\n",
    "                     160, 208, 261, 313, 352,\n",
    "                     143, 188, 220, 273, 314,\n",
    "                     154, 200, 244, 289, 325,\n",
    "                     171, 221, 270, 326, 358,\n",
    "                     163, 216, 242, 281, 312,\n",
    "                     160, 207, 248, 288, 324,\n",
    "                     142, 187, 234, 280, 316,\n",
    "                     156, 203, 243, 283, 317,\n",
    "                     157, 212, 259, 307, 336,\n",
    "                     152, 203, 246, 286, 321,\n",
    "                     154, 205, 253, 298, 334,\n",
    "                     139, 190, 225, 267, 302,\n",
    "                     146, 191, 229, 272, 302,\n",
    "                     157, 211, 250, 285, 323,\n",
    "                     132, 185, 237, 286, 331,\n",
    "                     160, 207, 257, 303, 345,\n",
    "                     169, 216, 261, 295, 333,\n",
    "                     157, 205, 248, 289, 316,\n",
    "                     137, 180, 219, 258, 291,\n",
    "                     153, 200, 244, 286, 324]).reshape(30,5).astype(int),\n",
    "                          columns=ages)\n",
    "rat_weights.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = rat_weights.T.plot(legend=False, color='LightSeaGreen')\n",
    "sns.despine()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "$$Y_{i,j} \\sim \\text{Normal}(\\alpha_i + \\beta_i (x_j - \\bar{x} ), \\sigma)$$\n",
    "\n",
    "$$\\alpha_i \\sim \\text{Normal}(m_a, s_a)$$\n",
    "\n",
    "$$\\beta_i \\sim \\text{Normal}(m_b , s_b)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_rats = rat_weights.shape[0]\n",
    "rat_index, age, weight = pd.melt(rat_weights.reset_index(), id_vars='index').values.astype(int).T\n",
    "age -= age.min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pymc3 import Normal, HalfCauchy, sample, Model\n",
    "\n",
    "with Model() as rat_model:\n",
    "    \n",
    "    # Hierarchical means\n",
    "    m_a = Normal('m_a', 150, sigma=100)\n",
    "    m_b = Normal('m_b', 20, sigma=10)\n",
    "    \n",
    "    # Hierarchical st.devs\n",
    "    s_a = HalfCauchy('s_a', 1)\n",
    "    s_b = HalfCauchy('s_b', 1)\n",
    "    \n",
    "    # Intercepts and slopes\n",
    "    α = Normal('α', m_a, sigma=s_a, shape=n_rats)\n",
    "    β = Normal('β', m_b, sigma=s_b, shape=n_rats)\n",
    "    \n",
    "    # Expected values\n",
    "    μ = α[rat_index] + β[rat_index]*age\n",
    "    \n",
    "    # Likelihood function\n",
    "    σ = HalfCauchy('σ', 1)\n",
    "    y = Normal('y', μ, sigma=σ, observed=weight)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's peek at a **directed acyclic graph (DAG)** of the model to make sure it looks right."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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       "<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n",
       " -->\n",
       "<!-- Title: %3 Pages: 1 -->\n",
       "<svg width=\"616pt\" height=\"238pt\"\n",
       " viewBox=\"0.00 0.00 616.39 238.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 234)\">\n",
       "<title>%3</title>\n",
       "<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-234 612.3887,-234 612.3887,4 -4,4\"/>\n",
       "<g id=\"clust1\" class=\"cluster\">\n",
       "<title>cluster30</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M190.6943,-91C190.6943,-91 414.6943,-91 414.6943,-91 420.6943,-91 426.6943,-97 426.6943,-103 426.6943,-103 426.6943,-154 426.6943,-154 426.6943,-160 420.6943,-166 414.6943,-166 414.6943,-166 190.6943,-166 190.6943,-166 184.6943,-166 178.6943,-160 178.6943,-154 178.6943,-154 178.6943,-103 178.6943,-103 178.6943,-97 184.6943,-91 190.6943,-91\"/>\n",
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       "</g>\n",
       "<g id=\"clust2\" class=\"cluster\">\n",
       "<title>cluster150</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M317.6943,-8C317.6943,-8 413.6943,-8 413.6943,-8 419.6943,-8 425.6943,-14 425.6943,-20 425.6943,-20 425.6943,-71 425.6943,-71 425.6943,-77 419.6943,-83 413.6943,-83 413.6943,-83 317.6943,-83 317.6943,-83 311.6943,-83 305.6943,-77 305.6943,-71 305.6943,-71 305.6943,-20 305.6943,-20 305.6943,-14 311.6943,-8 317.6943,-8\"/>\n",
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       "</g>\n",
       "<!-- α -->\n",
       "<g id=\"node7\" class=\"node\">\n",
       "<title>α</title>\n",
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       "</g>\n",
       "<!-- m_a&#45;&gt;α -->\n",
       "<g id=\"edge2\" class=\"edge\">\n",
       "<title>m_a&#45;&gt;α</title>\n",
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       "<title>σ</title>\n",
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       "<title>y</title>\n",
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       "<text text-anchor=\"middle\" x=\"365.6943\" y=\"-53.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">y ~ Normal</text>\n",
       "</g>\n",
       "<!-- σ&#45;&gt;y -->\n",
       "<g id=\"edge7\" class=\"edge\">\n",
       "<title>σ&#45;&gt;y</title>\n",
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       "<title>s_b</title>\n",
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       "<text text-anchor=\"middle\" x=\"387.6943\" y=\"-208.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">s_b ~ HalfCauchy</text>\n",
       "</g>\n",
       "<!-- β -->\n",
       "<g id=\"node6\" class=\"node\">\n",
       "<title>β</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"365.6943\" cy=\"-140\" rx=\"52.7911\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"365.6943\" y=\"-136.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">β ~ Normal</text>\n",
       "</g>\n",
       "<!-- s_b&#45;&gt;β -->\n",
       "<g id=\"edge4\" class=\"edge\">\n",
       "<title>s_b&#45;&gt;β</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M382.1428,-193.8314C379.7275,-185.9266 376.8432,-176.4872 374.1694,-167.7365\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"377.4374,-166.4541 371.1679,-157.9134 370.7429,-168.4997 377.4374,-166.4541\"/>\n",
       "</g>\n",
       "<!-- s_a -->\n",
       "<g id=\"node4\" class=\"node\">\n",
       "<title>s_a</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"219.6943\" cy=\"-212\" rx=\"74.9875\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"219.6943\" y=\"-208.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">s_a ~ HalfCauchy</text>\n",
       "</g>\n",
       "<!-- s_a&#45;&gt;α -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>s_a&#45;&gt;α</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M224.9935,-193.8314C227.2642,-186.0463 229.9689,-176.7729 232.4884,-168.1347\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"235.8837,-168.9933 235.3238,-158.4133 229.1637,-167.0332 235.8837,-168.9933\"/>\n",
       "</g>\n",
       "<!-- m_b -->\n",
       "<g id=\"node5\" class=\"node\">\n",
       "<title>m_b</title>\n",
       "<ellipse fill=\"none\" stroke=\"#000000\" cx=\"544.6943\" cy=\"-212\" rx=\"63.8893\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"544.6943\" y=\"-208.3\" font-family=\"Times,serif\" font-size=\"14.00\" fill=\"#000000\">m_b ~ Normal</text>\n",
       "</g>\n",
       "<!-- m_b&#45;&gt;β -->\n",
       "<g id=\"edge3\" class=\"edge\">\n",
       "<title>m_b&#45;&gt;β</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M506.5783,-197.4876C483.4076,-188.5796 453.2629,-176.8377 426.6943,-166 420.6784,-163.546 414.3503,-160.9104 408.14,-158.2925\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"409.1127,-154.9033 398.5398,-154.2218 406.3801,-161.3479 409.1127,-154.9033\"/>\n",
       "</g>\n",
       "<!-- β&#45;&gt;y -->\n",
       "<g id=\"edge5\" class=\"edge\">\n",
       "<title>β&#45;&gt;y</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M365.6943,-121.9902C365.6943,-111.2963 365.6943,-97.4994 365.6943,-85.3706\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"369.1944,-85.2612 365.6943,-75.2612 362.1944,-85.2613 369.1944,-85.2612\"/>\n",
       "</g>\n",
       "<!-- α&#45;&gt;y -->\n",
       "<g id=\"edge6\" class=\"edge\">\n",
       "<title>α&#45;&gt;y</title>\n",
       "<path fill=\"none\" stroke=\"#000000\" d=\"M260.7957,-123.0342C272.8755,-113.181 288.7559,-100.8155 303.6943,-91 311.1486,-86.1021 319.3657,-81.2457 327.3123,-76.8017\"/>\n",
       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"329.0258,-79.8538 336.1141,-71.9793 325.6623,-73.7148 329.0258,-79.8538\"/>\n",
       "</g>\n",
       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "<graphviz.dot.Digraph at 0x7da8e316d2e8>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pymc3 import model_to_graphviz\n",
    "\n",
    "model_to_graphviz(rat_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [σ, β, α, s_b, s_a, m_b, m_a]\n",
      "Sampling 2 chains: 100%|██████████| 3000/3000 [00:30<00:00, 98.43draws/s] \n"
     ]
    }
   ],
   "source": [
    "with rat_model:\n",
    "    rat_trace = sample(1000, cores=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<xarray.Dataset>\n",
       "Dimensions:  (chain: 2, draw: 1000, α_dim_0: 30, β_dim_0: 30)\n",
       "Coordinates:\n",
       "  * chain    (chain) int64 0 1\n",
       "  * draw     (draw) int64 0 1 2 3 4 5 6 7 8 ... 992 993 994 995 996 997 998 999\n",
       "  * α_dim_0  (α_dim_0) int64 0 1 2 3 4 5 6 7 8 9 ... 21 22 23 24 25 26 27 28 29\n",
       "  * β_dim_0  (β_dim_0) int64 0 1 2 3 4 5 6 7 8 9 ... 21 22 23 24 25 26 27 28 29\n",
       "Data variables:\n",
       "    m_a      (chain, draw) float64 153.6 156.2 155.7 157.8 ... 157.1 156.5 158.8\n",
       "    m_b      (chain, draw) float64 6.404 6.048 6.339 6.348 ... 6.067 5.993 6.247\n",
       "    α        (chain, draw, α_dim_0) float64 153.0 145.2 154.9 ... 141.5 156.1\n",
       "    β        (chain, draw, β_dim_0) float64 6.229 7.184 6.837 ... 5.417 5.885\n",
       "    s_a      (chain, draw) float64 9.49 9.6 13.53 11.86 ... 11.4 9.903 12.93\n",
       "    s_b      (chain, draw) float64 0.5667 0.44 0.7116 ... 0.4883 0.4016 0.6158\n",
       "    σ        (chain, draw) float64 5.612 6.565 6.327 6.501 ... 5.986 6.699 5.943\n",
       "Attributes:\n",
       "    created_at:                 2019-07-12T10:22:49.632205\n",
       "    inference_library:          pymc3\n",
       "    inference_library_version:  3.7"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from arviz import from_pymc3\n",
    "\n",
    "rat_output = from_pymc3(rat_trace)\n",
    "rat_output.posterior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from arviz import plot_trace\n",
    "\n",
    "plot_trace(rat_output.posterior, var_names=['m_a', 'm_b']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Informal Methods\n",
    "\n",
    "The most straightforward approach for assessing convergence is based on\n",
    "simply **plotting and inspecting traces and histograms** of the observed\n",
    "MCMC sample, as was done in the cell above. If the trace of values for each of the stochastics exhibits\n",
    "asymptotic behavior over the last $m$ iterations, this may be\n",
    "satisfactory evidence for convergence. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "CompoundStep\n",
      ">Metropolis: [σ]\n",
      ">Metropolis: [β]\n",
      ">Metropolis: [α]\n",
      ">Metropolis: [s_b]\n",
      ">Metropolis: [s_a]\n",
      ">Metropolis: [m_b]\n",
      ">Metropolis: [m_a]\n",
      "Sampling 2 chains: 100%|██████████| 3000/3000 [00:04<00:00, 658.55draws/s]\n",
      "The gelman-rubin statistic is larger than 1.4 for some parameters. The sampler did not converge.\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "from pymc3 import Metropolis\n",
    "\n",
    "with rat_model:\n",
    "    trace_bad = sample(1000, start={'m_a': 1000, 'm_b': -10}, step=Metropolis(), cores=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_trace(trace_bad, var_names=['m_a', 'm_b']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another *ad hoc* method for detecting lack of convergence is to examine\n",
    "the traces of several MCMC chains **initialized with different starting\n",
    "values**. Overlaying these traces on the same set of axes should (if\n",
    "convergence has occurred) show each chain tending toward the same\n",
    "equilibrium value, with approximately the same variance. Recall that the\n",
    "tendency for some Markov chains to converge to the true (unknown) value\n",
    "from diverse initial values is called *ergodicity*. This property is\n",
    "guaranteed by the reversible chains constructed using MCMC, and should\n",
    "be observable using this technique. Again, however, this approach is\n",
    "only a heuristic method, and cannot always detect lack of convergence,\n",
    "even though chains may appear ergodic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Only 200 samples in chain.\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "CompoundStep\n",
      ">Metropolis: [σ]\n",
      ">Metropolis: [β]\n",
      ">Metropolis: [α]\n",
      ">Metropolis: [s_b]\n",
      ">Metropolis: [s_a]\n",
      ">Metropolis: [m_b]\n",
      ">Metropolis: [m_a]\n",
      "Sampling 2 chains: 100%|██████████| 1400/1400 [00:02<00:00, 681.27draws/s]\n",
      "The gelman-rubin statistic is larger than 1.4 for some parameters. The sampler did not converge.\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "from pymc3 import Metropolis\n",
    "\n",
    "with rat_model:\n",
    "    \n",
    "    tr = sample(200, cores=2, start=[{'m_a':100}, {'m_a':200}], step=Metropolis(),\n",
    "                            discard_tuned_samples=False, random_seed=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7da8c84e1b38>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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mGmO6ApOBFikRsLp3ypYtS9myZd0dhlIqBdy2ZC8i60TkpOs0Y0xuoBswQhwVuiJy3jGvCFAPmONYfA5QzxhTOCUDV/fG8uXLGTBgAJUqVeLPP/90dzhKqWRK7kVVFYFAYKQxpjkQAgwXkXVAaeC0iEQBiEiUMeaMY/rFuBsyxngDca/bL5XMuFQKmzhxIkuXLgVg9OjRPPLII3h4eLg5KqXUnUpuA21WoAKwQ0TuBwYD840xybmB6QDgeJxH3Coj5SY9evSwn2/YsIFRo0a5LxilVLIlt2R/AojEUVUjIpuNMZcAHyAAKGmM8XCU6j2AEsDJRLb1OfBTnGml0ISfJvj4+ADw5JNPEhgYSLdu3dwckVIqOZJVsheRS8Bq4BGwet8ARYAjInIB2Ak861j8WawzgHhVOI5tBYuIv+sDOJWcuFTKq1ChAgBBQUG0a9eO5s2ba797pdKhpHS9/MIYcwqrtP2XMWafY1ZvYKgxZg/wM/C8iAS7zHvdGHMIeN3xWqVDuXLlImfOnNSvXx8R4fTp0zr8sVLp0G2rcUSkHxDvpqQicgxolsg6BwC/uw1OpQ2hoaEATJs2DYCLFy+SN29ymmeUUu6iV9CqJKtatSoAy5YtY9euXWzYsMHNESmlksqkxfpXY0w54Pjx48cpV66ce4NRNhGhcePGXL58mQMHDtjTlFJpg7+/P+XLlwco72j/tGnJXiWZMYaPP/6Y1q1b60FYqXRG71Sl7siDDz7Igw8+SHh4OPPnz3d3OEqpJNJkr+7YkCFDmDx5srvDUErdAa3GUXfMeUOTkiVLap29UumEJnuVbPv378cYc8frBQQEsH79em7evJkKUSmlEqLJXt2xAQMGABAcHIwxhl69et3R+g899BCNGzdm4sSJqRGeUioB2vVSJcvixYtp164dADly5CAsLCxJ64WEhJAnTx7uu+8+1q9fT/78+VMzTKUyFe16qVKVt3fcEaotJ0+epE+fPuzZs8eedvToUQDee+89TfRK3UOa7FWy+Pr60qZNGwAKFSqU4DJHjx7l22+/ZdeuXXaSd/7NmzcvFStWZPr06fcmYKVSwfXr1zHG8OOPP7o7lNvSZK+SpUiRIvzxxx90796d4ODgBJc5e/YsAM8//zyjR48G4L777mPMmDHUr1+fY8eOcepU0gc4vXjxIjdu3Lj74JVKIUFBQQAMGzbMzZHcniZ7dVe8vb2pW7duvOlBQUF06dIFgBo1anDixAnASvZDhw6lUKFC5M6dm4sXExz5Op5NmzZRpEgRxo8fn3LBK3WXihUrBsATTzzh5khuT5O9uivt2rWLd/eqPXv2EBgYaL+uVKmSndT/+ecfuzG3cOHC+Pv788ADD/Drr7/G27aI0L9/fzZt2oSfnx85c+Zky5YtqfdmlLpDWbJkoXjx4kRFRbk7lNvSZK/uSosWLahbty7R0dEAbNu2jVq1ajF8+HAA+vfvT+HChbl06RKXLl2iZcuWjBs3DrDq+hcsWMDmzZuZMmVKvG2HhobyxRdf0LBhQ4wx1KtXjytXrty7N6dSTXh4ON27d+e7775zdyh35dKlS5w9e5Z9+/bdfmE302Sv7lqJEiXo378/YPXAAZg3bx4AHTt2tJP9jh07iIqKokWLFgDUqVPHvnm5r68vX3/9tb3NKVOmMHfuXPt17969WbduHWfOnLkn70mlrrVr1zJt2jQGDhzo7lDuynlHm1O897F9Ozz4ICxZ4oaoEqZj46i7li1bNvbt28e1a9eoWbMmgH1a6+3tTefOnalbty7+/v4A9rUTkydP5sSJE5w7d44PPvgAgFdffRWAESNG2A2/RYsWtcfiCQgIIDw8nOzZs9+rt6dSgfPAXqBAATdHcnduOs5IPT09Y8/45RfYsAEefxzatIE//oiZd/48hIWB1R/+ntGSfWYRGAhJbAy9800Hsnr1ahYsWEClSpV49NFHyZo1K3Xr1qVgwYLUqlWLp556ikOHDgFQqlQpwBoy2Zm0H3/8cQBeeeUVgoKCOHfuHOHh4bRv356ffvoJgJEjR7Jy5UqyZ89OaGgoV69eTZX3o1LPvn37OHLkCF26dKFu3br07NnT3SHdlZtLlwLw+uuvx0w8exYmTLCelywJa9fGXqllS6hQAZ57DnbtgvHjrQNAahORNPcAygFy/PhxUSkkb16R7NlTZlvR0dbDoWrVqgLI2LFjpVu3bnLlypVYi1+5ckWWLl0qgJQpUybWvH379kndunUFsB8dOnSwnxcvXlzeeecdASQ4ONher3Tp0uLh4SE3b95Mmfek7om6detKu3bt3B1GwoKDRSIj5dixY4nnHtffW3CwrG3QwP6tyuLFIiVLisyeLeLhIfL11yKDBomASHi4iIicOXNG/siaVa6CSOvW1jwQGTgwRd7C8ePHnfGUkzh5VUv2mcHx43D1KoSHw/XryduGowqGdesgZ06YPt36mYJ916pdu3Yxffr0WHXtAIcPH+bRRx9lzpw5dl2+U7Vq1ahWrVqsaREREfbzs2fP2qNs5suXjxkzZrB8+XJOnjxJVFQUf/zxh904rNI+1yo4EYn1XbtVWBh4e8Pbb/PUU0/x2muvxV/m/HmoUQMGD7ZejxjBza1bY+Y//jicPm2V2tevhz59YqpqgoIgMpK1K1fSNjKSegULEjhrllWyh5j/r1SkyT6jmjwZ+vWDQYPAkSzZvBm++go+/RQSuRAqQVevQpUq8NNPsGOHddDo3h0qVgRg7969APzyyy8A8YZBcF5hGxYSQgPn+i6yZIn9M/z555/ZtWsXb731FgALFy7kt99+A+D999/nyy+/tJd94okn+Oqrr5L+XpRbuSb7QYMGpZ06+0WLrL9ffEH27NkJj/MbJSAAfvgBChWCFSusaZcv8xDwIpDbudy8eeDnZz0AnP8Lp09DqVLccFRbHQkMtKoha9WC1q3B0bEhVcUt6qeFB1qNc/ecp4cgkjOn9ffKFZFXX7WeGyOyc6d16vq//4lMnJj4tjZssNZZtEhk716RUqVitn35soiINC1UyD6d/Wf4cPu0VUQk5Nq1mFNdEBk92poRGSkiIn/++ac0adJEypcvLzVr1rTXi4qKksuO7Ts1bNhQmjRpIr/88os8+uijAkiPHj2S/TFdv349XrVThrV+vUilSiJurEYpVqyY9OrVS2TFCnnnuefE09NTZOVKkSZNRH77LUnbuHnzpvz++++yadOmpO102za5sXVr4vPDw0UqV7Z+mw8/HPNbdbVwoTW/aVPr77//irRtKwIyCCQniHz3Xfxtr1tnvbfJk0VAprhUV/7333/WMi+9JFK0aNLey23cqhrH7Yk9oYcm+xRQs6ZI7drWV1ytmkjp0tb006dFPvrImv7qqyL9+lnPS5USiYiwlpk82fqB7t1r/ajr17eWOXrUmv/88zHJ3ttbZN8+ublxo0z38LB+xCDy008i586JREVJ9Jw5Akj2rFlj1rv/fpFChUQCA6160M2b5bGmTaVly5Yi168n+rbatWsntWvXFhGROnXqCCCLFi1K9sdUu3bt+P/YGdW778Z8/iEhbgnB29tbXn/5ZRGQkY6kF9Wjh9We9PXXItu3W9+/S5uQiEh0dLTs27dPvvnmGylevLidMENDQ2+7zxNNmgggP/zwQ+wZO3dav//wcJEOHUS2bRMRSTjZT5pkfW5z51p/e/US8fOTnQ88IIDkzpbNKkwl5uhRkSZN5OuWLe3t79ixQ0RELmzbJt+NHi3Tpk2Tm5cviyThPSVGk31mVLCgSK1a1lf8++8iN27EzIuIEMmSJeYf38ND5M03rXmRkVZjro+PyJw5Il5e1jL16olERVnLBASIfP55zPr79omIyIL33pOi+fJJYOXKItOmiTz5pMjYsSL9+8tfICddzzYeecT6mzVrTJwg0Q0bisyYYe3H31+kbFmRWbPs0Hv06CEeHh6ydOlSqVOnjrzyyity5syZZH9MZcqUES8vr2Sv7zYBAVYJfdCgpK+zaZNIw4bWZ+0sVSYkODj27+UOhIeHS+/eveXUqVPWWV+cA/f//d//ybaJE0VAxjqS3vVGjUQaNxZ58UWRAgWs+N59115nzJgxct9998VqxH/kkUcEkICAgPhBbN4sMmWK9XzbNlntWKeUMbJ59Wpr+oEDMb/Fs2ftgs7NmGTp+qZEBg8W8fS0/geaN7cKQHnzyhzHmcD+/fsT/DwCAgJk3rx5EhERIbJli3z+wQf29jdu3CgiIsOHD7enzS5aVGTBgmR99iKa7DOHgACR5cutf9SpU2N+yCCye3f85R96SKRNG+tA4CyRjBljJXqwehSIWAl3796E97lqlciPP8Yqhb333nsS7XxdpozIww+L9OgRE8unn4pMn26t45w2YoTIkiUi5ctbrzt3Fjl8WKRuXet1kybW9ubPl7ffeiumuuiffyQsLEyWLl0qx44dS9bHVsXHR55Kq71DbmXo0JjPb/jwpCfnNWuspDVokMiHH8YcwJ3WrbO2+corVsl3zBi7us22dKlIs2YJ/i527dolgHzYvLm1nTJl4u8jKEhk3jyZULmy1cuqcGHrN/L22zHvydFrKzo6OlaSdz5GjRolgOzatSv+e3z9datXjIhI2bJyLc66F/z9rbMI528vLMxeNfjppwWQxo0bi3z7rcj331tVnrlyxZwd795tHSy++UamDxsmgBw5ciTBj7tZs2YCyMqVK0VE5MSJEzJy5EgpU6aMbNmyRUREXn7+eSmUK5d4584tL4HIBx8kuK2k0GSfGXTsaH2dw4ZZf8eOFenWTeSrr+KdEotI/GnXr4sUK2bV6XbvfutT0qTq3VskTx4rWYSEWAnc1cCBVl3liRPW640brdPpvXut5DVrljW/Xj2Rq1dFCheWSzNnyosvvigeHh5y7YUX5OLatQLIRNc2hxs3rLrV8uXlpqNr3Cf9+1vzAgKsZCUikZGRAkj+5Jbs4yaxe6VNG+s7zpVLpGtX6/mcOda8iAjrYPrGG1Zd+JIl1rTff7d+D5cvW3E7k6oj4YiIyKVLMdNnz7YO5GAlNlfPPmtVEbpWBUVHixw/LgGOZPM9WAl33jy71BwZGSkrVqywS+Nr166VwZ06SQhY1SQff2ztr2JFkUcfFZGY5OVa+r3//vulRIkSAshqZ0ndVdu2InXqWDFlySLy3HPinS+fAFIIrP09/bQ1L86B7EyPHgLIt6NGxS4wgbVNF9HR0Xa3YB8fH7l27ZrMnj1bfvrpJ3sZZ1XjL7/8IiEhIRLu0pblNG3cOHkHZA3Iv2BVZSWTJvvM4PHHRapXFxkwwGqQTSjB305K91mfNs36iTlKNckydKhVorpxw6rjB3mgenVpVKyYCEjkY4+JMUZGjBgRs86ZMyLlyokUKCDnHAmifbZs1rxWrayYtm6Vz8eNS7h+NjFXr8ZODqNHi3z5pdWukZrOnrUS2Jkzsc+IWrSw2jzA+pz8/KxEHDdJFSlildS9vKz4Dx2KmefaqDhwoDVt3Djr9dat1uv580XESm5HFiywSrpVq1olYkdVhGzfLmvy5ZMujs/zSxCJc7YVHBwsgHz67LN2/biEhVn908+csdp5nMm+alURiTlTaNmypZQtW1YAqVmzpgDSv3//mEZOEauA0rNn7KqgqVOlbpUq9vf8ccWK1m+jVSuREiXifdTn3nhDaoGMcf5OHA2r8uijdmcEpxkzZsQ6Y7h48aJ07dpVatWqJSIily9flmPHjlmfx5dfStasWQWQefPmxd5peLhI4cIx38ldFLQ02WcGDRta//xNm4rUqOHuaCxHj1o/sRo1RJL7XYaFWafSIiLNm8sexz9WF5dkVsjbW2rUqCFj33zTKrG51OPuX75cAJkzbJiVKD08rPUGDRKZMEE6ObYX9cILIm+9lXgchw5ZB5sRI6ztRETElLC9vKxS7sWLVgn1bg5uCXFWOfTvb+3D+d4//NCa7zjwJfioVMn6/CtUsErjIlbPK7ASo7OKLzTU+myMiTmgnT9vLffFFyIi8uNnnwmOEmisfTjOzEobYye+8Q89ZG1j2TIRR1XLuXPnBJBvQGTkSLl586ZcvnzZqs8WsQ5qjp5jR4yRupUqSc+ePe1tzp07V65fv57wAfq336zvzwJtzlIAACAASURBVDWutm3lmktPMECef/55OVekiMgLL1jvT0QiIiJk8eLFsn79epHPP5eBIHmc27hxw6pGbNYs3teybNmyWNs+deqUtGrVSnx9feXEiRMCyIABAyRr1qzy7rvvxlq2RYsWdtXO9evXJfrgQfkXZGm3bnf1U9FknxGFhorcd59VQrl8Oaa+G6wqnbRi+3arHjg5Zxpx7dsn/738sgCy7M8/rX9Wb2/xLVo0JgGASO7cVilcrKoCQH799Ver/tkYq3ph+3YRXBoJ/fyshjcRkU8+sbrDOZNQVJT1WWfNaiWkNm2s6pOQEJFvvrH2+dprVptJjhxWz5KAAKtqLCzMWs7ZwyIqyirVXr9uJdUFC2J1U03Q99/HSqoybpz1+to16/Urr8R89089ZZXy//3XKpk7P/dy5axSv4hVinaWiKOirM9x/HirLt25DxFr3WzZ7INgD0dj5JS4yX7aNJEdO6Sgh4c87/g8P3j/fWsb+fOL9O0rcv68HP/pJwFkKohs3iy//PKLALLXte4/MFDk0CGZ8/jjsZKj8+Fahx8aGiohISHWGWmcmMJAumfNKp84qmVcH/PLlLG6GzssXrzYnrdu2DB5DsQTYg7+M2dav5mFC+11hg0bJo899pgA0qZNGwHk2LFjdrVN/vz57W1+9dVXIiLy9ttvx4pj+vTpIiJSoUIF6fb889LdUfLvdhcJX5N9RjRhQuwSnpeX1d3ytdeSX4pOJ6Jc68r37pW3nn3W/ge67uj77EyGCxcuFECyOxPw6tV2g9xPTz5prxdcunT8UrGjb/aehQvlD7DOnrZssea99JK1/8uXrbrz7NmtEuyqVTHrDx0a08gMVpfXxYut54sWWfXsznnO6hCnkydjErUzuZ8/L7J/v/U+XIaOkLAw64Bau7Z1CX5cISHWWYnz+ganoCCr2g+skuulS/HXrVBB5JlnRETk+fLlrST1ww/WwaRPn1jvLw/IgIYNZfWqVXLCedAoV86a7+cn/zk+6zmO6pMFCxYIIP8mUA329fPPCyCVChWSzp07J5j4PTw8ZOjQodYByvV727lTNji6RLo+xo8fL4BMq1Ah1mf+9ddf28tUrVjRfh558qQVTHS0iKenbO7WTXbu3CnR0dHSqFEjO7H7+voKIAcOHJCSJUvG22+/fv1EROT999+PNf17xxlr/vz5pW/fvtK3VCkBpG3btvG/hyTSZJ/RuDawOUqwMn261dMiEzpy5Ii8/vrrAsi5U6esOtvChUWiosTf318AKVKkSLz1evXqZf/jXahWzfo8n3gipiuoo8tn/xo1JC9YZwbOz33t2pgNXbliXb8gYiWGihWtZebOteqhP/rI6kLaurXVGwmspP3SS7GTlLOkP3Om9XrqVGt7b75pvXbGlVjJ77HHRBo1sqp6XM2eLZIvX/zfx3//xe6Cm9DZ17lz1kGra1dZZ4wMqldPrrt2p1yyxF6/IMiQIUNir+/cdtmy8q/js17w2GMiIvLHH38IIBs2bIi32ysHDsgjIL3KlrUbQeM+ChcuLL1797YuFgMJe+opeadWLQkODpbQXbukQsGCsZbfsmWLADLJx8eK6f/+T0Ssi/py584tRYsWlTx58sQ6cxARkUOH5LzLdt555x2pXr16rDGcatSoIYcOHZIGLmPl/O9//5MsWbLYz+PGnzNnTrl586aA1btocL9+AshLzoJEMtx1sgfGA8cdG6mRwPyRcecBDwC7gEPAcqBIUvYlmuxv7/x5q8T13nvujiTNmDlzpgBy8OBBkdBQuejvb58B9O7dWwoVKiTR0dGxBk7r1q2b5M6dW/bu3SsRe/fG1MdHR1slVsc/e/m8eQWQ07NmWf8yTz5562AOHRL59VepVauWNGjQwJrWsqW17sCBMQ3o8+aJvP++1Qi4datVneOa/Dt3tnonffCBddBwnrW0apXwfk+etLZ1J33knY21jz+e+DLOq0ZLlYo5qDlFR1sHrm++sXsEzZo1S9566y25efOmjO/UyepSeeiQBIMsBTn39dciIrJ69WqBRHrUiIi0bi0bEkjygDz99NPi4+MjnTt3ti90Wj1lSqztdevWLdY6zkQ49o03Ev2cXEvm27dvl23btonUqiWbXbZTq1YtKVWqlHTv3l1+/PFHmTRpkr2+80yyUaNGsmLFinhxt2nTRgoUKGC/DggIEEC++eYbu15/2LBhSf764kqJZN8YKA34x032QD3gD+CEcx5ggCNAY8fr4cCPSdmXaLJXybB//34ZN26cXLhwQfbs2WP/A82aNUu6desm2bJlk5CQEAGkb9++IiLSuXNn8fHxue22nf+Yu3butC4gS8IVjhEREQLWCJ4iYpXYW7WKqdZIiOsVrrlzW33Pc+e2urCKiJw6Zc379NMkfSZJFhR0655YHTuKlCsnx379VTp37iz//PPPLTfn/LyWLFki5cuXl7///lu2rlsnlzw8RN55x15uw4YNAsiff/4ZbxsLFy6Uqc2ayceObT1Srpy93bffflt+/fVXeeCBB+SRRx4ROXhQpHBhWeRoA1i2bJlMnjzZLlWD1RsmIiJCPD095S1HXfyaNWvE19dXGjVqJCJWbyNPT0/p2LGjzJs3T7p06SKAyMiRstyxnUqVKkmpUqUkT5480t/ZnTeOBx98UFq0aCFvvvlmrESfK1cu2bJli6xfv96e9ueffwog8+fPl4EDBwogn3zyye2+sUSlWDVO3GQPeAEbgfKu84AGwF6X5QoBIYls09uR3F0fjTXZJ+LCBaueVSXIWVJyJlrXUpSzSgdHsu3QoYPkyJFDJk6cKBfjVn24cK6zfv16+eijj+SFF164ZQyXLl2SZ555RgCZMGGCPf3IkSNyLmdO6+rkuH7+2WrMBKvev1Yt6yrjBg2sac5ujEFB975//8svixQpYjdEOhscr169Kn5+fjJz5ky5ceOGdOnSJVZj50cffSSA/ORomB1atKgsaNTIPuM6ffq0jB49Wg7Huf7C2UXT9XHs99/t52fPnhURkbZt28r9depYbRaRkTLHMSzHwy7j21xzNGI7L/T7/fff5dy5czJ16lR7mSeffFKOHz8uDRs2FEA+dRxMR48eLYDky5dPihYpIoC0atVKcubMKdWrV7e/2+3bt4ufn58888wzUq5cOWnUqJHUrl1brl27Jn/99ZcEBgbKrl27ZPLkyQJWG8Wvv/4qYA31MWTIEDl06JCsXbtW8ufPn/iZThKkZrL/COgbdx7QEVgSZ90woEAC2xwV94t1PjTZJ+CDD6z6V2dPDCUiVkn66NGj9tj6gPj5+Ymnp6c0bdpURo8ebZf4AYmKirJLbhAzTomIyKFDh6RPnz52l0DXUpi3t7d9sEjI5cuX7YZAZww3b96UK1euCCAlS5SIdcWmLTLSOpA7zZljNYA+/LD1b+rs++4OZcuKgJRxNCCOHz9eREQOHjxov0/n+5swYUK8/+MzZ84IIB5ZskgOT8+YK6wTsX379njbGNavn9R1PA9dv17ks8/k57595btq1eRIwYKyadMm+f777wWwG35dDzhArP1++umnAkiWLFlEROTw4cMCyKBBg+zhN37++ed4cfTp00cAueFSBeQsqderV0+yZcsm4eHhEpbAd/zXX38JIG+99ZbdS2y+4xqGlJIqyR5oCKwCTALz7iTZa8k+qZwXKTm7CCqba4kerItw+jkavD744AP5999/7ZIaIIMHDxYRkSVLlggQawTFJo6Bs5yXszsvnpk+fboAMmbMmARjcDa2VapUKVYsgYGBIiLSv39/ARK8ijJRv/9u1ZknNmTFvbBzpxx1dHkFZLSjV8/ff/9tT7t48aIA8sUXX8R6702bNhURkSqOC5vuv/9+e7MRERESEBAgV52dDByc1TuzZ86U70A6V6hgnVG0amVdbOU6VARIKS8vAatxGJDLly/LoEGDpJDLSKzOA3RISIiMGTMm3vSzZ88KIF872hNERLZt2xZruWXLlsmsWbOkSpUqsZL91q1bBZDKlStLrly5Ev0YN27caG/r5MmTdswpKbWS/TvAGcc0fyASOA20IuFqnNA72E85TfZxhIXF/MB//93d0aQ5N2/eFGOMfderTz75RC5dumQ/j1tCc/6TO0tbCxculKJFi8pHH31kN6w566YDAgKkUqVKdom9f//+Urx4cfuiGCfn/uI+nCXFadOmCVhd9NIb5+cEMQ2IzsHInO8RkG+//dae9t1339kHtuvXr8uZM2diHeicFx5NcQ5a5rBq1SoBR0ProUPy4zffCCAFChSw2kv69xeZPVuCN24Uf8fZVvv27eXq1aty+PBhu5po8ODB8b7vGzduJPg7cF58VaZMGYl0XFR2/vz5WMvNnDlToqOjrUHeXBw6dEgA8fb2Fm9v70Q/w1OnTgkgjzl6I23dujVeFdbdSpU7VYnIhyJSQkTKiUg54BTQWkSWA/8COYwxjR2L9wbmJrIplRSHD1t/f/7ZuiOOisXT05MiRYpQv359GjduTOnSpbly5QoAO3bsSHCdN954gwmOe4UeOXKE8+fPM2rUKIoWLQrA+fPniYqKYsWKFSxatIh69eoBULduXc6ePcu+ffvsbV24cCHeHbMqOm7uEh4ezowZM+ybrBw/ftxexrmPtO6iy/2LjTEAHDx4EIDs2bNz8+ZNwPoePv74Y3r16kWvXr3w8vKylylevLj92jkN4MaNG7H21axZM8LDw2nSpAlUrky2PHkAq2BKzpzw+efw7LN8tGgRldu1w9PTk2LFihEaGkr58uXtm+E4vy+Iucl9tmzZGDp0qD39iy++ACBnzpyAdUN75/rOm+44vfjiixhjKFmyZKzpRYoUASA4OJhs2bIl+hmWLFmSq1evsnDhQgDuv/9+KlWqlOjyKS5u9k/oAXyBlcwjgXPAvgSW8Sd2fX4jYA9wGFgBFE3KvkRL9gm7ft26oCehC1+UiMTUrUdFRdnd+saNG2fX5cZ95M+f3x5Qa9CgQfHmf/nll3ZpfeLEiXL58mV5+OGHJSgoSMqUKSM+Pj7y9ttv2yXR+fPny6RJk+z1vRzVC/v375fu3bvb03/99Vc7Zj8/P+nTp4+Eh4dbV4OmYaGhoXap19n3vXXr1gLI0aNHpWjRovLLL78keXvOhljXRuyEOBsz8+fPH2u6c+TL3Llz2/3jB7kM+RwdHS1NmzYVQM6dO2dPd61qet95pa+IHDt2LOZiMIeBAwdK586dZfDgwXZbRVzOi6z8/PykZ8+eSX7/qUEvqlKZgnOArOjoaPnvv//sevbg4GB7XtxHmzZt5OjRo3ZCcX2sWbNGjhw5IoBMmzYt1r7Gjh1r30TDOYztt99+KyLWMM+u29m+fbt06NBBqlSpIqdOnZLr16/LpUuXJCQkRLy9vaVFixZSo0YNu0ohLXKtahnnMoDcX3/9JSNHjowZ3+YOOMe5GTt2bKzpmzdvltdee03OO8aucfZdj5vsP/zwQwEkW7Zscv/998eqlnFyfjdBQUH2tLlz58arxsko9IbjGcHPP4Pj9E8lbO3atVy4cAFjjF2FMnz4cCIjI9m9e7d9yvzqq6/a98ktWLAgFSpU4Lvvvou1rUaNGtGkSROCHffq9fb2jjV/yJAhnDhxggULFtC2bVvAOk2vXLkya9eutZebPXs2VatWJTg4mEKFClGyZEmyZ8/Os88+S8uWLXnooYe4ePGifR/fra43sE4jrly5Qt++fVm3bh3btm1j4sSJ9rwCBQowatQosmbNesfbdVZ5xK3G2b9/P5MmTSIsLAyAtm3bUq1aNXx9fWMt56wSOnfuHLNnz05wH7/99htLly6N9f2VKVOGF198kR49erB06dI7jjshIsLrr79u3Vc2jbrzb0jdW4cOwf79MHo0lC0LTzzh7ojSrHz58tnPPT09AasO9uTJkxQsWJAdO3YQFhZGkSJF6NixIx06dLATRq1atVixYgW1a9emZcuWNG/enL59+/J///d/QPybqDv38cQTT9CmTRsA2rVrB1j1/05+fn7kyJGDK1eukCdPHt577z3atm1LYGAgxYoVo0iRImzevNle3tfX13l2m+ICAwP5/vvvMcbQo0cPChcunKT1goKCuHHjBocPH8bX15dz587Z84oWLcqZM2cIDg5myJAhvPvuu9SvXz9J282SJQsTJ06Ml8SdN/t21ul7enommJSd88PDw6lUqRKfffYZVapUibWMt7e3fTB28vX1JX/+/Pj4+CQpzqRYuXIlkyZNYsqUKVy/fj3Ftpui4hb108IDrcaJUa9eTC+cW90UXMUzb948efPNN2MNkeCqQYMG1kBaDkeOHLF74ERGRkq2bNkErEHUErwjkoPzxucJPYYNGybHjh2TBg0aSLt27QSs7ollypSRbt26ydChQ8XDw0OMy/DAqcXZntC0aVO7KmnVqlW3XW/Hjh12m0RERIR4eXnJm47bWDp7GDn/Ll++/K7j/MwxlLJr1UtC9uzZI2PHjpUnnnhCVqxYcdf7vRuuvZXc6VbVOFqyT+t8fWH7dnjlFeje3d3RpCsdO3akY8eOic7fsmVLrNcVK1a0q388PDwYPnw47777Lm+88Qb33XdfottZvHix3YPDaeTIkZw/f54xY8bg6enJli1buHbtGnnz5mXLli0EBARQsGBBWrZsSdasWenQoQN169a9i3d7e4GBgQAsX76c4OBgunTpwqpVq4iKiooXvytnVVb+/PnJmjUrVatWZfv27UBM6dpZfeE8o0qqQ4cOkTNnTkqVKgXAunXrWLRoUaxtJ6ZGjRoUKlSIoUOH0qZNGx5++OE72ndKypUrl9v2nVRaZ5+WBAXBunWxp33zjVWu//ZbyJvXPXFlUs4E1KNHj1smMWdXRFdBQUH0798fgFGjRjF79my7yui3334jS5YsVKxYkRYtWvDee++xcuXKZMfZq1cvOyHfSlBQELlz58bLy4t+/fqxatUqsmfPfstE71wPYtotqlatyurVq9m3b1+8ZH+rrocJad68OaNGjbJfb9iwgdWrV2OMue22QkJC7DYO1y6d7uDsupmWabJPS+bNgw8/hCNHoFkzqFcPZsxwd1SZ3pIlS+54HWf/bafFixfbB4yBAwdy+PBhXn31VXt+d8dZ250my7Vr1zJlyhT++++/2y4bHBwcq2HayVlHDla17sqVK2O1G1SqVIkhQ4bYB79PPvmEpUuXUr16dTvZX7t2LVnxZ8uWLVYbQIECBQA4duzYbQ9Ca9asoX379sDtzwJSW3oo2Ws1Tlpy5gwsWQLt2sE//1jTunWDhx6CMmXcG1sm1LVrVwIDA+nVq1eS19m8eTOXLl3i5s2bsRoLs2fPjjEGT09PQkJCqFChQqz1ChYsyBtvvMHq1auTvK8hQ4bYjcGuCTsx77zzDj179rT351xv0aJFdOrUCYDJkyfTp08f5s6dy9NPPw1AzZo1qVmzpr2d0qVLU7p0aQBy5MgBWAeJSpUq3XHSy5s3L0uWLGHixInkyJGDV155BbAuPHNeCJUY1wTv7pJ9iRIlaN68eapXxd0NTfZpyblzkC+fVcJ//32oXh0++QSKF3d3ZJmSp6cngwYNStKyQ4cOpVSpUvF6lvTv35+JEyfayWjfvn34+Pjg4+NDnz59Yi3rvJr3v//+o3z58rctrc6ePdtOtrfqARIVFcUHH3wAwFtvvQXEvjr05ZdftpP9zp07gdhXzJ47d45cuXKRx3Elq6sKFSowbNgwunfvzocffnjLeBPy/fff4+fnx4EDByhWrJg9vUePHrGuNE6Ia4LPnTv3He87JeXIkYNVq1a5NYbb0Wocd5owwRr6IDTUen32rFWCX7ECRoyAJ5+EjRvhDhu91L03ZsyYeMkbYhKS869zSAXXbqKuAgMDqVatGq+99lqi+zp69CgPP/wwp06dsq8duFXJ/sCBA4waNYpRo0bZBxTXapwrV67Yfd0ffPBBIHZX09dee40GDRokuO2SJUuycuXKBN97Uvj6+vLxxx/Ttm1bQkND8fT0pFWrVrRq1eq26zoPhosWLUrS8qlJRPj111/ZtWuXW+O4FU3291p0tNXgeu0aDBpkVds4LVwILqUblf7FTfZvvvkmkHC//dmzZ9vVAA888ACRkZEJbnPlypWsXLmShx56iGeffRa4dbJ3Nt62bt2aOnXqAFZSnzp1qt224KwOatSoEdWqVbPrzsGqUilfvnyC246IiGDTpk13VY3y1ltv0b59e0JDQ8mbNy/Lli1j8uTJt13PuU8PD49k7zulGGPo1KmT/fmmRVqNcy9ERFgXQ7VpA0OGQOHC4PxnmjULnPWc770HLVq4L06V4ho1akS/fv0YPXo0ENPYG/eKXLBK7CdPngTAx8cHT09PmjVrFq8ev2LFirzwwgt8//33REVFUalSpVgDal24cMEenAtikv37779vVzOVL1+eUqVK2YO55c2bl+DgYDZt2sTSpUspW7asvf7Jkye5//77E3x/zsbV9evX38GnEtuVK1e4fv06YWFhd9SrpUqVKvTu3ZuHHnoo2fvOVOJ2vE8LDzLaRVVHj8ZcGAXWTSlAJFs266YVKtPAceHNwYMH481zvdHG0KFDY12ks3btWilatKhMnjz5ltt33g3JGGMPpbt582Z55pln5OTJk/ZyzrH3fX19Zfny5RIVFWXfeKRq1ar2ctHR0eLh4ZHouOvOYYDbt29/x5+FU/v27aV27dry6aefyssvv5zs7bgbCYzfc6/p2DjuFreh6dNPwRgYPx7SwCmoSj2hoaF07do1Xj96Z28WV64Nss7hkJ02bNjA+fPnGTFiBJMnT7a7RkZERPDDDz+wdetWZs2aRVhYGIMHD6ZBgwZs3LgRsOrF58yZY3edhJgG3S1btvDII4+QJUsW++zgwIEDzJw5044/KioqwWonsIb3XbVqFbNmzbqjz8VVvnz5uHr1KgMHDkxS9U1a9d9//3HgwAF3h5Eorca5F6ZMsZL7u++Cnx9kz27V3asM77PPPmPWrFmULVuWli1bUr9+fYoWLWr3onHlWu/tHIsfYMaMGezcuRMfHx+OHz9O7969OXz4MOPHj0dEeOmll2Jt5/Tp03h5eTF69GiioqISrNNOqGeNa1XQiRMnAKs+/Msvv6RRo0aJvsfmzZvf4hO4vbx583Lp0iWWLVtG69at72pb7lS1alV3h3BLmuxTmwj8+Sd06gQuVwqqzClLliyJDnRWqFAhqlSpYt8UBKxSb7du3QCrJ0/cq3XjXtnbpUsXSpQoQeXKlXnggQc4duwYtWvXJleuXPFuQNKiRQueeuope1q1atXYvn079erVs0v+OXLkuGXPoJRQrlw5rl27Rps2bXj99dfjXZCmUoYm+9R24wY8/bTVOKsyPWdvnIQ4x/Jp164dp06d4vHHH2fs2LH2/H///TdeQ2nc5O/sNdO1a1e6du1K27ZtuX79Og888EC8/SU0REPdunXJlSuXneyvXLlCQEAAlStXTrWrVN944w3+97//ER0dfdsLqVTyaZ19asueHb77zuozrzItZ1Lu3LkznTt3vuWyefPm5dq1a/Tp04fdu3fbJd05c+bcdj/OgdwAdu3axZ9//snIkSPv6IKfHDly2Mn+77//platWuzfvz/J698pZ3uBj4/PHQ+3oJJOS/apLSAAChWy7p2pMh1nfXlCg6Ul5sknn6R27dqUKFGCEiVKUL16dV599dVE+5OXKFHCbgNw1p+fO3fOvirWtaomKRo2bEgZx/AccQdBU+mXJvvU9vDDUKcOzNX7rWdGHTt2JDQ0lJdffvmO1onrVhcOrV69mnz58tk3SgcoVqwYK1asQERi9ZlPCucQwxCT7BPrjaPSD032qSkqCvz9oUMHd0ei3MTHx8celyY195GQMskcPC8yMpJly5axb98+Ll26hDEm0eEdVPqhyT41nTxpXT0bZ4RDpdKyqKgoXnjhBftmJ97e3rcdblilffoNpqZNm6y/iVxqrlRa5OXlxf79+6lRowYA33zzjZsjUilBk31qmj8f8uSB2rXdHYlSd6RIkSL2IGtxb9it0idN9qlp7Fj44QfIqrVlKv2pV68e9erVY8eOHe4ORaUATfYp5cgR6NwZQkLgl1+s0S1LlrQuqFIqHWrZsiVPPfWU9n3PIExil267kzGmHHA8KbcmSzP+9z9rPHpX7dvHn6aUUqnE39/feRV1eRHxd52nJfuUNnw4vPGG9fzvv90ailJKOWllckq5fBkefBAcN6mgY0dwuchFKaXcSZN9SvHyAtchTm8xJKxSSt1rWo2TEoYPt7pYfvmluyNRSqkEJSnZG2PGG2OOG2PEGFPDMa2gMWapMeagMWa3MWa+MaawyzoPGGN2GWMOGWOWG2OKJL6HdO6bb8AxhohSSqVFSS3ZLwCaAidcpgnwsYhUEZFawFHgQwBjDfE3E+grIj7AGue8DOXmTVi+3Kqvr1/f3dEopVSikpTsRWSdiJyMM+2yiPztMmkT4Bxe734gXETWOV5/C3S6y1jTnk8+Aedt1Fq1cm8sSil1CynSQGuMyQL0AZxjo5bB5SxARC4ZY7IYYwqIyOU463oDcQfLLkV6kD8/+PrC7NngctMIpZRKa1KqN86XQAgwKRnrDgBGplAc99arr0Lv3qAjAiql0ri7zlLGmPFAZaCziEQ7JgcQU6WDMaYQIHFL9Q6fA+XjPJrcbVyp7uBB6/6ymuiVUunAXWUqY8wYoD7wPxG54TLrXyCHMaax43VvIMFbNYlIsIj4uz6AU3cTV6qLjLRGsnzpJXdHopRSSZKkahxjzBfAk0Ax4C9jTCBWg+tQ4BCwwXGPzeMi0kFEoo0xzwOTjTHZAX+gayrEf+9FRICfn1Wqb9rU3dEopVSSJCnZi0g/oF8CsxK9i7KIbABqJjOutCc6GoyBn3+GHTusYRG6dXN3VEoplSRa4ZwUV69Cy5ZQogSsXw/e3jBsj/CnjgAACF9JREFUmDVEglJKpQM6Nk5SDB0aM4JlvXqQL59VyldKqXRCk31S7Nxp/d2yBRo0cG8sSimVDJrsk+Kpp8DHRxO9Uird0mSfFB06WHeiUkqpdEobaG9lzhxo3txqiE0vt0dUSqkEaMk+MTt3wltvQe7cescppVS6p8k+MZMnw+nTsHmz9rxRSqV7Wo2TmFOnrCERfH3dHYlSSt01TfaJOXUKSqWPkZaVUup2tBonMVOmaPWNUirD0GSfGL3NoFIqA9FqnIRMmABzExyRWSml0iVN9gmZMAEWL3Z3FEoplWI02ccVHAxnz0KNGu6ORCmlUowm+7gOHLD+3nefe+NQSqkUpMk+LucIl1qyV0plIJrs4zp1CooU0bFwlFIZiib7uD74AE6e1D72SqkMRZO9099/Q/Xq8OWXkC2bu6NRSqkUpRdVAVy/bg1lDHDhgntjUUqpVKAle4DVq62/Tz8NAwa4NxallEoFWrIHmDYNChaEGTOsG5UopVQGoyV7gOHDrStmNdErpTIoLdkD1Kzp7giUUipVacn+yhWYOtXqX6+UUhmUJvsdO6BHD9i7192RKKVUqtFk/88/1gVUDzzg7kiUUirVaLLftg2qVQNvb3dHopRSqSbzNtCGhVml+oMHrRuLK6VUBpZ5S/YvvACPPgqHD4OPj7ujUUqpVHXbZG+MGW+MOW6MEWNMDZfpPsaYjcaYQ46/lZMyz63efRcaNLD61M+bZ0374gt49VX3xqWUUqksKSX7BUBT4ESc6d8CX4mID/AVMDmJ81Lf6dOwebP1uHIFwsOthD56tFV988kn1nIvvgidOkHJkvc0PKWUutduW2cvIusAjMuQv8aYIkA94BHHpDnAJGNMYcAkNk9ELsbdvjHGG4jbOlrqzt6Gi8BAKOWyupcX3LgR87pCBfj6azh/HurX16GMlVKZQnIbaEsDp0UkCkBEoowxZxzTzS3mxUv2wABgZDLjiC9rVujZE9q1s0r0q1dbyb55c6uk36ULlC5tPZRSKpNIC71xPgd+ijOtFLA2WVvLlw+mTIl53blzzPNu3ZK1SaWUSu+Sm+xPAiWNMR6OkrsHUMIx3dxiXjwiEgwEu04zWrWilFIpKlldL0XkArATeNYx6Vlgh4hcvNW8uw1WKaVU8iSl6+UXxphTWFUrfxlj9jlm9QZeN8YcAl53vCYJ85RSSt1jSemN0w/ol8D0A4BfIuskOk8ppdS9l3mvoFVKqUxEk71SSmUCmuyVUioT0GSvlFKZQFq4qCohHgCn9FaBSimVZC450yPuPCMi9zaaJDDGNCa5V9AqpZRq4hzXzCmtJnsvoAFwFoi6w9WdQy00AdL6qUF6ihU03tSUnmKF9BVveooV7i5eD6A4sFVEbrjOSJPVOI4g1912wQS4DLVwSkT8Uyqm1JCeYgWNNzWlp1ghfcWbnmKFFIn3aEITtYFWKaUyAU32SimVCWiyV0qpTCAjJvtg4D3iDJucRqWnWEHjTU3pKVZIX/Gmp1ghleJNk71xlFJKpayMWLJXSikVhyZ7pZTKBDJUsjfG+BhjNhpjDjn+VnZzPOONMceNMWKMqZGUON31HowxBY0xS40xB40xu40x840xhR3zHjDG7HLEtNwYU8RlvUTn3YOYFzj2vcMYs9YYU8cxPc19vi77H+n6e0jDn62/MeaAMWan49E6rcZrjMlujPnGGHPYGLPHGPOdY3qa+x0YY8q5fKY7HZ/z5XsSr4hkmAewCujqeN4VWOXmeBoDpQF/oEZS4nTXewD+v717eZWjiOI4/qlcUcRAJESDkcQYn6AgRDe+UBeiLnyAC81GRVzEv0AQQRACgoISQ1aajQZBQUEQEQWz0wsxCWoWPiAvFDGPVUCE6HFRZe44cu8oODPFnfOFoatPLepXp0+frq5qalbjzoHzl/CG+p/CP+C2Zn8Ou1p50boJaV41UH4Q+3r1b2tvMz7CEVzfuW//FrOjNE1TL7bjFQtrkGt7joMh7a9ixyT0TrxzY3Taxerq9Vw7n2vnF3Wg7eyNs5TOnvqAh/Gpum3FNwP2NTjdyovWTUHvY9jbq39xHj7H5X/FQ8++XSTZd6cXK9s1XDlk7zIOhjSei+PqIGDsepfTNM56/BgRv0M7/tTsPbGUzi76UEpZgafxATaoI1FN0wmsKKWsHlE3Ka2vl1KOYhse169/X8BbEXFowNa1b7G7TentLKVc2KneK3ASz5dS9pZS9pS6kWKvcTDIA03HvknoXU7JPvn/eA2nsWPaQkYREU9FxAY8q049dUcp5WZ15Ltz2lr+A7dHxA2q7qLfWDgHm7A/Im7CM3hPHfH3zpPYNanGllOyP4ZLSylz0I7rmr0nltI59T6UUl7GVXgkIv7AUVw2UL8GERGnRtRNlIh4E3epuwT25t87cC0OlVIOq7safowrderbiDjWjr+pD6lbR2ialt4jOIO3m955nMCv+ouDs5RS1qlxsbuZxp4Xlk2yj4hfcABbmmmL+rQ/Pj1V/2QpndPuQyllG27EQ7GwPeqXOL+9GsNWvPMv6satdWUpZf3A+f04he78GxEvRsS6iNgYERvVB9I96ptIj769oJSyqpULHlX91l0stOmiz3B303u1Osf9nc7iYIgn8GFEnGRCeWGSCxLj/qmjp3n1Qs/jminr2a7e2GfwMw6O0jmtPuA6BL5tgXUA77e6W/A1vscn2tcOo+rGrHctvmhtH1C/Vtjcq3+HtB+2sGDfo283YT++wkG8i0s617untb0P9/UeB63de4dsY9Wb2yUkSZLMAMtmGidJkiRZnEz2SZIkM0Am+yRJkhkgk32SJMkMkMk+SZJkBshknyRJMgNksk+SJJkBMtknSZLMAH8CtqN0a7MxQ1UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(tr.get_values('m_a', chains=0), 'r--')\n",
    "plt.plot(tr.get_values('m_a', chains=1), 'k--')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A principal reason that evidence from informal techniques cannot\n",
    "guarantee convergence is a phenomenon called ***metastability***. Chains may\n",
    "appear to have converged to the true equilibrium value, displaying\n",
    "excellent qualities by any of the methods described above. However,\n",
    "after some period of stability around this value, the chain may suddenly\n",
    "move to another region of the parameter space. This period\n",
    "of metastability can sometimes be very long, and therefore escape\n",
    "detection by these convergence diagnostics. Unfortunately, there is no\n",
    "statistical technique available for detecting metastability."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Formal Methods\n",
    "\n",
    "Along with the *ad hoc* techniques described above, a number of more\n",
    "formal methods exist which are prevalent in the literature. These are\n",
    "considered more formal because they are based on existing statistical\n",
    "methods, such as time series analysis.\n",
    "\n",
    "PyMC and ArviZ currently include a handful formal convergence diagnostic methods.  A commonly-applied metric is the Gelman-Rubin statistic [Gelman and Rubin (1992)](http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ss/1177011136). This diagnostic uses multiple chains to check for lack of convergence, and is based on the notion that if multiple chains have converged, by definition they should appear very similar to one another; if not, one or more of the chains has failed to\n",
    "converge.\n",
    "\n",
    "The Gelman-Rubin diagnostic uses an analysis of variance approach to assessing convergence. That is, it calculates both the between-chain varaince (B) and within-chain varaince (W), and assesses whether they are different enough to worry about convergence. Assuming $m$ chains, each of length $n$, quantities are calculated by:\n",
    "\n",
    "$$\\begin{align}B &= \\frac{n}{m-1} \\sum_{j=1}^m (\\bar{\\theta}_{.j} - \\bar{\\theta}_{..})^2 \\\\\n",
    "W &= \\frac{1}{m} \\sum_{j=1}^m \\left[ \\frac{1}{n-1} \\sum_{i=1}^n (\\theta_{ij} - \\bar{\\theta}_{.j})^2 \\right]\n",
    "\\end{align}$$\n",
    "\n",
    "for each scalar estimand $\\theta$. Using these values, an estimate of the marginal posterior variance of $\\theta$ can be calculated:\n",
    "\n",
    "$$\\hat{\\text{Var}}(\\theta | y) = \\frac{n-1}{n} W + \\frac{1}{n} B$$\n",
    "\n",
    "Assuming $\\theta$ was initialized to arbitrary starting points in each chain, this quantity will overestimate the true marginal posterior variance. At the same time, $W$ will tend to underestimate the\n",
    "within-chain variance early in the sampling run. However, in the limit as $n \\rightarrow  \\infty$, both quantities will converge to the true variance of $\\theta$. In light of this, the Gelman-Rubin statistic monitors convergence using the ratio:\n",
    "\n",
    "$$\\hat{R} = \\sqrt{\\frac{\\hat{\\text{Var}}(\\theta | y)}{W}}$$\n",
    "\n",
    "This is called the potential scale reduction, since it is an estimate of the potential reduction in the scale of $\\theta$ as the number of simulations tends to infinity. In practice, we look for values of $\\hat{R}$ close to one (say, less than 1.1) to be confident that a particular estimand has converged. In PyMC, the function `gelman_rubin` will calculate $\\hat{R}$ for each stochastic node in the passed model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<xarray.Dataset>\n",
       "Dimensions:  (α_dim_0: 30, β_dim_0: 30)\n",
       "Coordinates:\n",
       "  * α_dim_0  (α_dim_0) int64 0 1 2 3 4 5 6 7 8 9 ... 21 22 23 24 25 26 27 28 29\n",
       "  * β_dim_0  (β_dim_0) int64 0 1 2 3 4 5 6 7 8 9 ... 21 22 23 24 25 26 27 28 29\n",
       "Data variables:\n",
       "    m_a      float64 1.003\n",
       "    m_b      float64 1.001\n",
       "    α        (α_dim_0) float64 0.9998 1.0 0.9997 1.001 ... 1.0 1.001 1.0 0.9994\n",
       "    β        (β_dim_0) float64 1.001 1.0 1.001 1.002 ... 1.0 1.002 0.9997 1.0\n",
       "    s_a      float64 1.002\n",
       "    s_b      float64 1.002\n",
       "    σ        float64 1.0"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from arviz import rhat\n",
    "\n",
    "rhat(rat_trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the best results, each chain should be initialized to highly\n",
    "dispersed starting values for each stochastic node.\n",
    "\n",
    "When calling the `plot_forest` function using nodes with\n",
    "multiple chains, the $\\hat{R}$ values can be plotted alongside the\n",
    "posterior intervals by specifying `r_hat=True`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x475.2 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from arviz import plot_forest\n",
    "\n",
    "plot_forest(rat_trace, var_names=['s_a', 's_b', 'σ'], r_hat=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Autocorrelation\n",
    "\n",
    "In general, samples drawn from MCMC algorithms will be autocorrelated. This is not a big deal, other than the fact that autocorrelated chains may require longer sampling in order to adequately characterize posterior quantities of interest. The calculation of autocorrelation is performed for each lag $i=1,2,\\ldots,k$ (the correlation at lag 0 is, of course, 1) by: \n",
    "\n",
    "$$\\hat{\\rho}_i = 1 - \\frac{V_i}{2\\hat{\\text{Var}}(\\theta | y)}$$\n",
    "\n",
    "where $\\hat{\\text{Var}}(\\theta | y)$ is the same estimated variance as calculated for the Gelman-Rubin statistic, and $V_i$ is the variogram at lag $i$ for $\\theta$:\n",
    "\n",
    "$$\\text{V}_i = \\frac{1}{m(n-i)}\\sum_{j=1}^m \\sum_{k=i+1}^n (\\theta_{jk} - \\theta_{j(k-i)})^2$$\n",
    "\n",
    "This autocorrelation can be visualized using the `plot_autocorr` function in ArviZ or PyMC3:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 993.6x331.2 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from arviz import plot_autocorr\n",
    "\n",
    "plot_autocorr(rat_trace, var_names=['m_a']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 993.6x331.2 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_autocorr(trace_bad, var_names=['m_a']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Effective sample size\n",
    "\n",
    "The main concern with high autocorrelation is that the effective sample size of the resulting chain can be greatly reduced. Hence, it will take more draws to control sampling variation, relative to a less correlated sample. \n",
    "\n",
    "The effective sample size is estimated using the partial sum:\n",
    "\n",
    "$$\\hat{n}_{eff} = \\frac{mn}{1 + 2\\sum_{i=1}^T \\hat{\\rho}_i}$$\n",
    "\n",
    "where $T$ is the first odd integer such that $\\hat{\\rho}_{T+1} + \\hat{\\rho}_{T+2}$ is negative.\n",
    "\n",
    "The issue here is related to the fact that we are **estimating** the effective sample size from the fit output. Values of $n_{eff} / n_{iter} < 0.001$ indicate a biased estimator, resulting in an overestimate of the true effective sample size."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<xarray.Dataset>\n",
       "Dimensions:  (α_dim_0: 30, β_dim_0: 30)\n",
       "Coordinates:\n",
       "  * α_dim_0  (α_dim_0) int64 0 1 2 3 4 5 6 7 8 9 ... 21 22 23 24 25 26 27 28 29\n",
       "  * β_dim_0  (β_dim_0) int64 0 1 2 3 4 5 6 7 8 9 ... 21 22 23 24 25 26 27 28 29\n",
       "Data variables:\n",
       "    m_a      float64 2.21e+03\n",
       "    m_b      float64 2.829e+03\n",
       "    α        (α_dim_0) float64 2.23e+03 2.389e+03 ... 2.292e+03 2.064e+03\n",
       "    β        (β_dim_0) float64 2.37e+03 2.315e+03 ... 2.427e+03 2.099e+03\n",
       "    s_a      float64 2.041e+03\n",
       "    s_b      float64 2.04e+03\n",
       "    σ        float64 1.216e+03"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from arviz import effective_sample_size\n",
    "\n",
    "effective_sample_size(rat_trace)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As with $\\hat{R}$, effective sample size estimates can optionally be added to forest plots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgIJACAjkACAOgs+0DaOTWdqyZvy86p6XEPBQBYIo4b9wAW0mVX35LNl1+fjWtXZXLX7mw+58yc+9hTxj0sAGCRq9bauMcw0xEZzHnvvDLf2HdXPv+lqXz0RU/MxLrV2bpjKs98+2fzsHWr85FffOKRWA0AC6dGuO+i+sHGWIzy+EmyjE+x7d13Z05esyIT61YnSSbWrc7Ja1Zm7747xzwyAGCxW5aBdMn5Z+VdL3xCdnxtb7bumEqSbN0xla/csTfveuETxjw6AGCxW5an2PYzBwlgyXKKjVGMfIptWQdSMngV28279mTD2pU5cfWKI714ABaGQGIUAgmAZUkgMQqTtAEAjjSBBADQEUgAwJK2ZcvF2TRxeo459thsmjg9dcyxPznqMo9oIFXVp6rqGUdymQAAs9my5eJccOFLsufxL8iGX/lw9jz+BTlm1QN+f9RIOqKTtKvqU0ne2Fr7o3kuwsQ6ABKTtDlEmyZOz57HvyArNj7q7sumJ6/Lzg+/ZvKuvV8/db7LnfMIUlWtqqoPVNUNVXVtVV06x12ePDyS9I9V9br5DgwAYC6TN23N8evPuMdlx68/I+0bex48ynIP5Z/VPjXJCa21M5Kkqk6Y4/ZnJHlykhVJrqyqvxjhiBIAwKw2njaRPdtvuMcRpL3bb0h968p/HmW5hzIH6dokp1fV26vqx5LsneP2726t7Wut3ZHk/Ul+aJQBAgDM5jWbX5HdV7wt05PXpd25L9OT1+XLl79hd/vm9K+Pstw5jyC11m6qqocnOTvJ05K8rqoe2VqbPoTlV5wLBgAWyPOeN5iL/fLNr87kpVuz8bSJ3LX7X/5Du+vOi0dZ7pyTtKtqfZJdrbXdVbUqyReTnNFa++IBbvupJNNJnpHk+CR/keRlh3GKTUwBkJikzWhG/kvahzIH6ZFJXl9VSXJskt88UBzN8DdJPpHklCQfMP8IAFhq/C82ABYjR5AYhf/FBgBwpB12IFXV06vqmgO8PX0hBjiqnVPTuWrytuycOpQ55QAAy/wU22VX35LNl1+fjWtXZXLX7mw+58yc+9hTjuQqAFgYTrExipFPsS3LQDrvnVfmG/vuyue/NJWPvuiJmVi3Olt3TOWZb/9sHrZudT7yi088EqsBYOEIJEZhDtJs9u67MyevWZGJdauTJBPrVufkNSuzd9+dYx4ZALDYLctAuuT8s/KuFz4hO762N1t3TCVJtu6Yylfu2Jt3vfAJYx4dALDYLctTbPuZgwSwZDnFxijMQZrLzqnp3LxrTzasXZkTV6840osHYGEIJEYhkABYlgQSozBJGwDgSBNIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgcRRa+fUdK6avC07p6bHPRQAFpnjxj0AGIfLrr4lmy+/PhvXrsrkrt3ZfM6ZOfexp4x7WAAsEtVaG/cYZlpUg2FxOe+dV877vttv251bbv/XI0Urjjsml7/4SZlYtzpbd0zlnLd+JtP77rrX/U5ZsyLrT1h1yOu55Pyz5j1G4B5qhPv6WcIoj58kTrFxlDppzcpMrFudJJlYtzonrVk55hEBsJg4xcaSMcrRmYs+fmPefMXWuz+/9fY92bpj6u4jSLfevueA93vO4zbkwqc8dN7rBWBpcoqNo5I5SLDoOcXGKEY+xSaQOGrtnJrOzbv2ZMPalTlx9YpxDwe4J4HEKAQSAMuSQGIUJmkDABxpAgkAoCOQAOAotGXLxdk0cXqOOfbYbJo4PVu2XDzuIS0qXuYPAEeZLVsuzgUXviSrzn5RNpx7RvZsvyEXXPiSJMnznveTYx7d4nDEJ2lX1U8neWkG8fWQDCZKbWmtPf8Q7m5iHQCJSdoLatPE6dnz+BdkxcZH3X3Z9OR1Wfm5d2fb1s+PcWRHzKKcpP3WJM9qrU0keWGSvz7EOAIA7gOTN23N8evPuMdlx68/I5M3bZ3lHkefhQikv26t7c/PP0jymKpaswDrAQDmYeNpE9m7/YZ7XLZ3+w3ZeNrEmEa0+CxEINUBPt63AOsBAObhNZtfkd1XvC3Tk9el3bkv05PXZfcVb8trNr9i3ENbNBZikvYjq+qM1toNSX4myedaa3cswHoAgHnYPxH75ZtfnclLt2bjaRN500VvMEF7hoWYpH12kv+W5FuS7Ezyc621mw7x7ibWAZCYpM1o/KsRAJYlgcQoFuWr2AAAljSBxFFr59R0rpq8LTunpsc9FAAWGX9Jm6PSZVffks2XX5+Na1dlctfubD7nzJz72FPGPSwAFglzkFhSznvnlYd9n+237c4tt9/zKNGK447J5S9+UibWrc7WHVM5562fyfS+u+5131PWrMj6E1Yd1vouOf+swx4jcC/mIDEKc5BgPk5aszIT61YnSSbWrc5Ja1aOeUQALCZOsbGkzOfozEUfvzFvvuKefz7/1tv3ZOuOqbuPIN16+54D3vc5j9uQC5/y0HmNFYClyyk2jkrmIMGi5xQbo/B3kGC+dk5N5+Zde7Jh7cqcuHrFuIcD3JNAYhQCCYBlSSAxCpO0AQCONIEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANARSAAAHYEEANA5btwD2K+qjtu2bdu4hwHAIrBp06ZTk2xvre07nPv5WUIy/8fPTNVaO1LjGUlVnZrEoxqA/Ta11r5wOHeoqkcluXZhhsMSc9iPn5kWzRGkJNuTbDrI9euT/HmS7x/edqmyHYvHctiGZHlsx3LYhmR5bMdi2ob5rP/rw/eLYfz3tcX0vbsvzbbdI30NFk0gDQ+DfWG266tq/4fbRynCcbMdi8dy2IZkeWzHctiGZHlsxzLYhjuH75fq+OdtGXzv5mWhttskbQCAjkACAOgIJACAzlIKpNuTvGr4fimzHYvHctiGZHlsx3LYhmR5bMdS34alPv5RHK3bviDbvWhe5g8AsFgspSNIAAD3CYEEANBZMoFUVQ+tqiur6sbh+4lxj+lwVNUDq+qPq+ofquq6qvpwVT1o3OMaRVW9sqpaVT1i3GM5XFW1oqp+t6q2VtXfVtXvjXtM81FVz6iqq6vqmuHj6tnjHtNcquqNVbWtf+wstX38QNuxFPfz2b4fM65fMvv5UnsMzWU++8p8r1tMDrYfVdX3VtW1w234WFWdOON+87puVq21JfGW5JNJnj/8+PlJPjnuMR3m+Ncm+cEZn78hyf8c97hG2J7vSvInSSaTPGLc45nH+N+S5KL86zy8deMe0zy2oZLctv/rn+RRSaaSHDPusc0x7icl2ZDBH4Z9xIzLl9Q+fqDtWIr7+Wzfj+F1S2o/X2qPofl+bw62nfO9bjG9zbYfDZ/z/jHJk4aXvzzJ/xp+PK/rDjqOcX8hDvGLdWIGs9OPHX5+7PDzB417bCNs048m+cS4xzHPsR+f5MoM/jXMvZ5UF/tbkvsNHz/3G/dYRtyOSvLVJE8cfv5vktw47nEdxvhnhsWS3ccPtg8spf38AD+El9R+vpQfQ4fzvTnYds73unFv3yFs/48m+USS707ydzMu//Ykdww/ntd1B3tbKqfYNiS5pbV2Z5IM339xePmSU1XHJLkgyUfHPZZ5enWS97bWluo/F35IBmHxyqr6XFV9qqqeNO5BHa422NN/PMkfVtVkksuSvGC8o5q3ZbWPJ/bzMVh2j6FZHGw753vdotXtRw/O4GhmkqS19pUkx1TV2hGum9VSCaTl5q1J7kjytnEP5HBV1VkZ1Ph/H/dYRnBcktOSXN1ae3ySX0vy4aq6/3iHdXiq6rgkL03yzNbaxiTnJLmkqu433pExZD+H0Y1tP1oqgXRzklOq6tgkGb4/eXj5klJVb0wykeS81tpd4x7PPPxAktOTbKuqL2TwX5T/tKp+eKyjOjyTSfYleV+StNb+KslXkjx0nIOah8ckObm19tkkGb7/epKHj3VU87Ns9vHEfj4my+oxdBAH2875XrcoHWA/+uckG2dc/+0ZHEzfNcJ1s1oSgdRa25nkmiQ/MbzoJzL47f/L4xvV4auq1yZ5XJJzW2t7xz2e+Witvb61dnJr7dTW2qlJtid5amvtY2Me2iEbHl79syRPSQav7Mjg/Pw/jnNc87A9yfqqeliSVNXDk3xHkn8a66jmYbns44n9fFyW02PoYA62nfO97r4b/aGbZT+6KsnKGVMifj7JpSNeN7txT746jElapyf5qyQ3Dt8/bNxjOszxn5mkJfmHDB6k1yT5yLjHdQS26wtZ5JM3Zxn3aUk+leRvk/xNkqeNe0zz3I7nDbfh2uHbueMe0yGM+S0Z/MDdl+RLSa4fXr6k9vEDbcdS3M9n+350t1kS+/lSewzN93tzsO2c73WL6e1g+1GS7xs+521N8vHMeAXyfK+b7c2/GgEA6CyJU2wAAPclgQQA0BFIAAAdgQQA0BFIAAAdgQQA0BFIAAAdgQQA0Pn/ejymHWuv0X0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x475.2 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_forest(rat_trace, var_names=['s_a', 's_b', 'σ'], ess=True);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both low $n_{eff}$ and high $\\hat{R}$ indicate **poor mixing**.\n",
    "\n",
    "It is tempting to want to **thin** the chain to eliminate the autocorrelation (*e.g.* taking every 20th sample from the traces above), but this is a waste of time. Since thinning deliberately throws out the majority of the samples, no efficiency is gained; you ultimately require more samples to achive a particular desired sample size. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Diagnostics for Gradient-based Samplers\n",
    "\n",
    "Hamiltonian Monte Carlo is a powerful and efficient MCMC sampler when set up appropriately. However, this typically requires careful tuning of the sampler parameters, such as tree depth, leapfrog step size and target acceptance rate. Fortunately, the NUTS algorithm takes care of some of this for us. Nevertheless, tuning must be carefully monitored for failures that frequently arise. This is particularly the case when fitting challenging models, such as those with high curvature or heavy tails."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fortunately, however, gradient-based sampling provides the ability to diagnose these pathologies. PyMC makes several diagnostic statistics available as attributes of the `MultiTrace` object returned by the `sample` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<xarray.Dataset>\n",
       "Dimensions:               (chain: 2, draw: 1000, log_likelihood_dim_0: 150)\n",
       "Coordinates:\n",
       "  * chain                 (chain) int64 0 1\n",
       "  * draw                  (draw) int64 0 1 2 3 4 5 6 ... 994 995 996 997 998 999\n",
       "  * log_likelihood_dim_0  (log_likelihood_dim_0) int64 0 1 2 3 ... 147 148 149\n",
       "Data variables:\n",
       "    energy_error          (chain, draw) float64 0.3258 0.06674 ... -0.1434\n",
       "    step_size_bar         (chain, draw) float64 0.2802 0.2802 ... 0.2804 0.2804\n",
       "    depth                 (chain, draw) int64 4 5 5 4 4 4 4 4 ... 4 4 4 5 4 4 4\n",
       "    tune                  (chain, draw) bool True False False ... False False\n",
       "    tree_size             (chain, draw) float64 15.0 31.0 31.0 ... 15.0 15.0\n",
       "    lp                    (chain, draw) float64 -631.2 -632.0 ... -642.5 -637.2\n",
       "    mean_tree_accept      (chain, draw) float64 0.8265 0.8256 ... 0.4996 0.9935\n",
       "    max_energy_error      (chain, draw) float64 0.4505 0.4895 ... 1.412 -0.3699\n",
       "    energy                (chain, draw) float64 656.1 661.5 ... 674.9 669.1\n",
       "    diverging             (chain, draw) bool False False False ... False False\n",
       "    step_size             (chain, draw) float64 0.2522 0.2522 ... 0.3655 0.3655\n",
       "    log_likelihood        (chain, draw, log_likelihood_dim_0) float64 -2.706 ... -2.84\n",
       "Attributes:\n",
       "    created_at:                 2019-07-12T10:22:50.191933\n",
       "    inference_library:          pymc3\n",
       "    inference_library_version:  3.7"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rat_output.sample_stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- `mean_tree_accept`: The mean acceptance probability for the tree that generated this sample. The mean of these values across all samples but the burn-in should be approximately `target_accept` (the default for this is 0.8).\n",
    "- `diverging`: Whether the trajectory for this sample diverged. If there are many diverging samples, this usually indicates that a region of the posterior has high curvature. Reparametrization can often help, but you can also try to increase `target_accept` to something like 0.9 or 0.95.\n",
    "- `energy`: The energy at the point in phase-space where the sample was accepted. This can be used to identify posteriors with problematically long tails. \n",
    "- `energy_error`: The difference in energy between the start and the end of the trajectory. For a perfect integrator this would always be zero.\n",
    "- `max_energy_error`: The maximum difference in energy along the whole trajectory.\n",
    "- `depth`: The depth of the tree that was used to generate this sample\n",
    "- `tree_size`: The number of leafs of the sampling tree, when the sample was accepted. This is usually a bit less than $2 ^ \\text{depth}$. If the tree size is large, the sampler is using a lot of leapfrog steps to find the next sample. This can for example happen if there are strong correlations in the posterior, if the posterior has long tails, if there are regions of high curvature (\"funnels\"), or if the variance estimates in the mass matrix are inaccurate. Reparametrisation of the model or estimating the posterior variances from past samples might help.\n",
    "- `tune`: This is `True`, if step size adaptation was turned on when this sample was generated.\n",
    "- `step_size`: The step size used for this sample.\n",
    "- `step_size_bar`: The current best known step-size. After the tuning samples, the step size is set to this value. This should converge during tuning."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the name of the statistic does not clash with the name of one of the variables, we can use indexing to get the values. The values for the chains will be concatenated.\n",
    "\n",
    "We can see that the step sizes converged after the 2000 tuning samples for both chains to about the same value. The first 3000 values are from chain 1, the second from chain 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [σ, β, α, s_b, s_a, m_b, m_a]\n",
      "Sampling 2 chains: 100%|██████████| 6000/6000 [00:30<00:00, 194.64draws/s]\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with rat_model:\n",
    "    trace = sample(1000, tune=2000, init=None, cores=2, discard_tuned_samples=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(trace['step_size_bar']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `NUTS` step method has a maximum tree depth parameter so that infinite loops (which can occur for non-identified models) are avoided. When the maximum tree depth is reached (the default value is 10), the trajectory is stopped. However complex (but identifiable) models can saturate this threshold, which reduces sampling efficiency.\n",
    "\n",
    "The `MultiTrace` stores the tree depth for each iteration, so inspecting these traces can reveal saturation if it is occurring."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sizes1, sizes2 = trace.get_sampler_stats('depth', combine=False)\n",
    "fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True, sharey=True)\n",
    "ax1.plot(sizes1)\n",
    "ax2.plot(sizes2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also check the acceptance for the trees that generated this sample. The mean of these values across all samples (except the tuning stage) is expected to be the same as `target_accept`, which is 0.8 by default."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "accept = trace.get_sampler_stats('mean_tree_accept', burn=1000)\n",
    "sns.distplot(accept, kde=False);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8051433646771582"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accept.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Divergent transitions\n",
    "\n",
    "Recall that simulating Hamiltonian dynamics via a symplectic integrator uses a discrete approximation of a continuous function. This is only a reasonable approximation when the step sizes of the integrator are suitably small. A divergent transition may indicate that the approximation is poor.\n",
    "\n",
    "If there are too many divergent transitions, then samples are not being drawn from the full posterior, and inferences based on the resulting sample will be biased\n",
    "\n",
    "If there are diverging transitions, PyMC3 will issue warnings indicating how many were discovered. We can obtain the indices of them from the trace."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([   0,    1,    2,    3,    4,   10,   11,   13,   15,   19,   21,\n",
       "         23,   27,   30,   33,   35,   37,   40,   43,   47,   51,   53,\n",
       "         55,   57,   58,   60,   62,   65,   69,   71,   73,   75,   77,\n",
       "         80,   86,   93,  112, 3000, 3001, 3002, 3003, 3004, 3010, 3013,\n",
       "       3018, 3022, 3024, 3029, 3032, 3035, 3036, 3038, 3040, 3041, 3044,\n",
       "       3048, 3050, 3052, 3060, 3063, 3072, 3079, 3087, 3130])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diverging_ind = trace['diverging'].nonzero()[0]\n",
    "diverging_ind"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the location of the divergences are distributed differently than the samples as a whole, this is an indication that the posterior is not being well explored."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7da8c2fe47b8>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from arviz import plot_pair\n",
    "\n",
    "plot_pair(trace, var_names=['m_b', 's_b'], divergences=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian Fraction of Missing Information\n",
    "\n",
    "The Bayesian fraction of missing information (BFMI) is a measure of how hard it is to\n",
    "sample level sets of the posterior at each iteration. Specifically, it quantifies **how well momentum resampling matches the marginal energy distribution**. \n",
    "\n",
    "$$\\text{BFMI} = \\frac{\\mathbb{E}_{\\pi}[\\text{Var}_{\\pi_{E|q}}(E|q)]}{\\text{Var}_{\\pi_{E}}(E)}$$\n",
    "\n",
    "$$\\widehat{\\text{BFMI}} = \\frac{\\sum_{i=1}^N (E_n - E_{n-1})^2}{\\sum_{i=1}^N (E_n - \\bar{E})^2}$$\n",
    "\n",
    "A small value indicates that the adaptation phase of the sampler was unsuccessful, and invoking the central limit theorem may not be valid. It indicates whether the sampler is able to *efficiently* explore the posterior distribution.\n",
    "\n",
    "Though there is not an established rule of thumb for an adequate threshold, values close to one are optimal. Reparameterizing the model is sometimes helpful for improving this statistic."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.81042525, 0.78520842])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from arviz import bfmi\n",
    "\n",
    "bfmi(rat_output)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another way of diagnosting this phenomenon is by comparing the overall distribution of \n",
    "energy levels with the *change* of energy between successive samples. Ideally, they should be very similar.\n",
    "\n",
    "If the distribution of energy transitions is narrow relative to the marginal energy distribution, this is a sign of inefficient sampling, as many transitions are required to completely explore the posterior. On the other hand, if the energy transition distribution is similar to that of the marginal energy, this is evidence of efficient sampling, resulting in near-independent samples from the posterior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7da8cc1b9278>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from arviz import plot_energy\n",
    "\n",
    "plot_energy(rat_output)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the overall distribution of energy levels has longer tails, the efficiency of the sampler will deteriorate quickly."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Goodness of Fit\n",
    "\n",
    "Checking for model convergence is only the first step in the evaluation\n",
    "of MCMC model outputs. It is possible for an entirely unsuitable model\n",
    "to converge, so additional steps are needed to ensure that the estimated\n",
    "model adequately fits the data. One intuitive way of evaluating model\n",
    "fit is to compare model predictions with the observations used to fit\n",
    "the model. In other words, the fitted model can be used to simulate\n",
    "data, and the distribution of the simulated data should resemble the\n",
    "distribution of the actual data.\n",
    "\n",
    "Fortunately, simulating data from the model is a natural component of\n",
    "the Bayesian modelling framework. Recall, from the discussion on\n",
    "imputation of missing data, the posterior predictive distribution:\n",
    "\n",
    "$$p(\\tilde{y}|y) = \\int p(\\tilde{y}|\\theta) f(\\theta|y) d\\theta$$\n",
    "\n",
    "Here, $\\tilde{y}$ represents some hypothetical new data that would be\n",
    "expected, taking into account the posterior uncertainty in the model\n",
    "parameters. \n",
    "\n",
    "Sampling from the posterior predictive distribution is easy\n",
    "in PyMC. The `sample_posterior_predictive` function draws posterior predictive checks from all of the data likelhioods."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior predictive distribution of weight uses the same functional\n",
    "form as the data likelihood, in this case a normal stochastic. Here is\n",
    "the corresponding sample from the posterior predictive distribution (we typically need very few samples relative to the MCMC sample):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 500/500 [00:00<00:00, 627.10it/s]\n"
     ]
    }
   ],
   "source": [
    "from pymc3 import sample_posterior_predictive\n",
    "\n",
    "with rat_model:\n",
    "    weights_sim = sample_posterior_predictive(rat_trace, samples=500)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It can be convenient to combine the MCMC trace and the posterior predictive samples in the same `InferenceData` object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "rat_output = from_pymc3(trace=rat_trace, posterior_predictive=weights_sim)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Inference data with groups:\n",
       "\t> posterior\n",
       "\t> sample_stats\n",
       "\t> posterior_predictive\n",
       "\t> observed_data"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rat_output"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The degree to which simulated data correspond to observations can be evaluated in any number of ways. It is often most convenient to compare them visually, which allows for a qualitative comparison of model-based replicates and observations. If there is poor fit, the true value of the data may appear in the tails of the histogram of replicated data, while a good fit will tend to show the true data in high-probability regions of the posterior predictive distribution. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1008x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 4, figsize=(14, 4))\n",
    "\n",
    "for obs, sim, ax in zip(weight[:4], weights_sim['y'].T[:4], axes):\n",
    "    ax.hist(sim)\n",
    "    ax.vlines(obs, *ax.get_ylim(), 'red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For a large number of observations, the `plot_ppc` function in ArviZ creates a single plot that summarizes the relationship between simulated and observed data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([<matplotlib.axes._subplots.AxesSubplot object at 0x7da8d21d7da0>],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from arviz import plot_ppc\n",
    "\n",
    "plot_ppc(rat_output, alpha=0.05, figsize=(12, 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([<matplotlib.axes._subplots.AxesSubplot object at 0x7da8c32d0a20>],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_ppc(rat_output, alpha=0.05, figsize=(12, 6), kind='cumulative')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## To Learn More\n",
    "\n",
    "- Betancourt, M. 2017. [A Conceptual Introduction to Hamiltonian Monte Carlo](https://arxiv.org/abs/1701.02434). arXiv.org.\n",
    "- Gelman, Andrew, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin. 2013. Bayesian Data Analysis, Third Edition. CRC Press.\n",
    "- Vehtari, Aki, Andrew Gelman, Daniel Simpson, Bob Carpenter, and Paul-Christian Bürkner. 2019. [Rank-normalization, folding, and localization: An improved Rˆ for assessing convergence of MCMC](https://arxiv.org/abs/1903.08008), arXiv.org.\n"
   ]
  }
 ],
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   "language": "python",
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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   "cite_by": "apalike",
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   "eqNumInitial": 0
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